While construction showed some resilience in March, the market for new homes has been stifled by a glut of foreclosed properties.

In addition, the overall housing market has been hindered by high levels of unemployment, despite a modest pick up in hiring this year. Homebuilders have also had trouble financing projects, as credit remains tight.

"The underlying trends, as far as we can tell, are about flat, at a very low level, having dropped at the turn of the year," said Ian Shepherdson, chief U.S. economist at High Frequency Economics.

Shepherdson said construction won't recover until new home sales start to pick up, which hasn't happened yet. But he said an increase in home buyer traffic over the past two months was "positive."